Question

If x is an acute angle of a right triangle and sin x = 3 / 7, find the exact value of the trigonometric function cos x.

• A. 2 $\sqrt{(}10)/3$
• B. 2 $\sqrt{(}10)/7$
• C. 3 $\sqrt{(}10)/3$
• D. 5 $\sqrt{(}10)/3$

Answer 1

The correct option is A

2 $\sqrt{(}10)/3$

If sin x = opposite / hypotenuse = 3 / 7, then we can say that opposite = 3 and hypotenuse = 7 and find the adjacent side using Pythagora's theorem.

$hypotenus{e}^2=adjacen{t}^2+opposit{e}^2$

$7^2$ = $adjacen{t}^2+3^2$

adjacent = $\sqrt{40}=2\sqrt{10}$

We now use trigonometric ratios to find

cos x = adjacent / hypotenuse = 2 $\sqrt{(}10)/7$

cot x = adjacent / opposite = 2 $\sqrt{(}10)/3$